The ideal generated by σ-nowhere dense sets

The ideal generated by σ-nowhere dense sets

In this paper, we consider the ideal Iσ generated by all σ-nowhere dense sets in a topological space. Properties of this ideal and its relations with the Volterra property are explored. We show that Iσ is compatible with the topology for any given topological space, an analogue to the Banach categor...

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Bibliographic Details
Main Authors: Jiling Cao, Sina Greenwood
Format: Article
Language:English
Published: Universitat Politècnica de València 2006-10-01
Series:Applied General Topology
Subjects:
Compatible
Ideal
Resolvable
σ-nowhere dense
Volterra
Weakly Volterra
Online Access:http://polipapers.upv.es/index.php/AGT/article/view/1928
Description
Summary:In this paper, we consider the ideal Iσ generated by all σ-nowhere dense sets in a topological space. Properties of this ideal and its relations with the Volterra property are explored. We show that Iσ is compatible with the topology for any given topological space, an analogue to the Banach category theorem. Some applications of this result and the Banach category theorem are also given.
ISSN:1576-9402
1989-4147

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